Commons

No simultaneityPart of the concept of absolute time was the assumption that itwas valid to say things like, “I wonder what my uncle in Beijing isdoing right now.” In the nonrelativistic world-view, clocks in LosAngeles and Beijing could be synchronized and stay synchronized,so we could unambiguously define the concept of things happeningsimultaneously in different places. It is easy to find examples, however,where events that seem to be simultaneous in one frame ofreference are not simultaneous in another frame. In figure i, a flashof light is set off in the center of the rocket’s cargo hold. Accordingto a passenger on the rocket, the parts of the light traveling forwardand backward have equal distances to travel to reach the frontand back walls, so they get there simultaneously. But an outsideobserver who sees the rocket cruising by at high speed will see theflash hit the back wall first, because the wall is rushing up to meetit, and the forward-going part of the flash hit the front wall later,because the wall was running away from it.i / Different observers don’t agreethat the flashes of light hit thefront and back of the ship simultaneously.We conclude that simultaneity is not a well-defined concept.This idea may be easier to accept if we compare time with space.Even in plain old Galilean relativity, points in space have no identityof their own: you may think that two events happened at thesame point in space, but anyone else in a differently moving frameof reference says they happened at different points in space. Forinstance, suppose you tap your knuckles on your desk right now,count to five, and then do it again. In your frame of reference, thetaps happened at the same location in space, but according to anobserver on Mars, your desk was on the surface of a planet hurtlingthrough space at high speed, and the second tap was hundreds ofkilometers away from the first.Relativity says that time is the same way — both simultaneityand “simulplaceity” are meaningless concepts. Only when the relativevelocity of two frames is small compared to the speed of lightwill observers in those frames agree on the simultaneity of events.The garage paradoxOne of the most famous of all the so-called relativity paradoxeshas to do with our incorrect feeling that simultaneity is well defined.The idea is that one could take a schoolbus and drive it at relativisticspeeds into a garage of ordinary size, in which it normally would not80 Chapter 4 Relativity